Parsing of 置いてあったってしょうがない

Question

Harry Potter is surprised to see that he has Christmas presents:

「ねぇ、これ見てくれる？　プレゼントがある」
Hey look at this. There are presents.
「ほかに何があるっていうの。大根なんて置いてあったってしょうがないだろ？」
What else should be there? You wouldn't expect there to be radishes, right?

Whilst the meaning is pretty clear I'm not 100% sure about the grammar in 置いてあったってしょうがない. Obviously the base of this is 置いてある. The first question is what is this って? I see two options:

1. It's quotative and short for 置いてあったというしょうがない
2. It's part of 置いてあったって meaning 'even if it's been put there'.

I'm favouring option 2.

Next, as far as I know しょうがない is normally preceded by something in te-form. Is that role also fulfilled by あったって? Why not just あって?

Finally, verb-てしょうがない is normally taught as meaning that "doing verb can't be helped", but that clearly is not the meaning here. Jisho also gives "there's no reason to ..." as an additional meaning. Presumably this meaning uses the same grammar? Is there some underpinning way of thinking that links these two meanings?

Answer 1

しょうがない is a reduced form of しようがない, where しよう is synonymous to し[方]{かた}, “way of doing.” The underpinning imagery is that the situation at hand is such that there is nothing you can’t do about it, or there is no way to deal with it. [V て-form]-しょうがない, with a verb of emotion, means you have said emotion so much that you don’t know how to deal with it. [V て-form]-もしょうがない means doing the action of the verb doesn’t change the situation and there is still no way to deal with it, so there is no point in doing it.

[V た-form]-ってしょうがない is a colloquial variation of [V て-form]-もしょうがない.